Topologically multiplexed optical data communication

ABSTRACT

Systems and methods for encoding information in the topology of superpositions of helical modes of light, and retrieving information from each of the superposed modes individually or in parallel. These methods can be applied to beams of light that already carry information through other channels, such as amplitude modulation or wavelength dispersive multiplexing, enabling such beams to be multiplexed and subsequently demultiplexed. The systems and methods of the present invention increase the number of data channels carried by a factor of the number of superposed helical modes.

CROSS-REFERENCE OF PRIOR APPLICATION

This application claims priority to U.S. patent application Ser. No.60/608,657 filed on Sep. 10, 2004 and is incorporated herein byreference.

FIELD OF THE INVENTION

The present invention relates generally to methods for transformingconventional beams of light into helical modes and superpositions ofhelical modes.

BACKGROUND OF THE INVENTION

Optical data communication typically involves modulating the amplitudeand wavelength of a beam of laser light, and detecting that modulationdownstream. The present invention is directed to a complementaryapproach to conveying information on a beam of light based on theproperties of helical optical modes.

A helical mode is characterized by the corkscrew-like topology of itswave fronts, which can be described by a real-valued phase function:φ({right arrow over (ρ)})=lθ  (1)

where {right arrow over (ρ)}=(ρ,θ) is the position in a plane transverseto the beam's axis, with θ being the polar angle, and l is an integralwinding number known as the topological charge that describes the pitchof the helix. This phase establishes the beam's topology through thegeneral expression for the magnitude of the electric field in acollimated beam,E _(l)({right arrow over (ρ)})=υ_(l)({right arrow over(ρ)})exp(iφ({right arrow over (ρ)}))exp(i φ _(l)),  (2)

where υ_(l)({right arrow over (ρ)}) is the real-valued amplitude profileand φ_(l) is an arbitrary constant phase. A general superposition ofhelical modes can be written as

$\begin{matrix}{{E\left( \overset{\rightarrow}{\rho} \right)} = {\sum\limits_{l = {- \infty}}^{\infty}\;{{E_{l}\left( \overset{\rightarrow}{\rho} \right)}.}}} & (3)\end{matrix}$

If it is assumed that all the beams in the superposition have the sameamplitude profile, υ({right arrow over (ρ)}) perhaps with differentamplitudes, α_(l), then

$\begin{matrix}{{{E\left( \overset{\rightarrow}{\rho} \right)} = {\sum\limits_{l = {- \infty}}^{\infty}{\alpha_{l}{\upsilon\left( \overset{\rightarrow}{\rho} \right)}{\exp\left( {{i\varphi}\left( \overset{\rightarrow}{\rho} \right)} \right)}{\exp\left( {i\phi}_{l} \right)}}}},} & (4)\end{matrix}$

with normalization Σ_(l=−∞) ^(∞)|α_(l)|²=1. For the practicalapplications, only a limited set of the α_(l) will be non-zero.

SUMMARY OF THE INVENTION

The present invention relates in part to methods for transformingconventional beams of light into helical modes and superpositions ofhelical modes. The present invention also involves detecting helicalmodes and methods for parallel data extraction from superpositions ofhelical modes. The ability to encode and decode information carried in abeam's topology leads naturally to methods for topological datacommunication. A slight elaboration on this theme yields methods formultiplexing and demultiplexing beams of light that also carryinformation through other channels, such as amplitude modulations.

These and other objects, advantages and features of the invention,together with the organization and manner of operation thereof, willbecome apparent from the following detailed description when taken inconjunction with the accompanying drawings, wherein like elements havelike numerals throughout the several drawings described below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plot showing radial intensity profiles for superpositions ofhelical modes created from a conventional flat-top beam with acomputer-designated phase-only diffractive optical element;

FIG. 2( a) is a representation of a helical beam with topological chargel being converted to a conventional non-helical beam by a DOE encoding atopological charge of −l; and FIG. 2( b) is a representation of ahelical beam if the DOE does not exactly cancel the input beam'shelicity, wherein the resulting beam still has a dark focus and will notbe detected by the photodetector.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The wave fronts of a helical beam may all meet along the optical axis ata topological singularity known as an l-fold screw dislocation.Conventional beams, by contrast, have no such defect. Introducing such adefect therefore transforms a conventional beam into a helical beam.There are numerous ways to accomplish this transformation and one of themost straightforward methods of transforming a conventional beam into ahelical beam is to sculpt the phase of the conventional beam's wavefronts according to Equation (1) discussed previously. This can beaccomplished by passing the beam of light through a piece of transparentmaterial with a helical surface relief, with the resulting local phaseshift being proportional to the local thickness of the material.

Another method for accomplishing this task is to employ a phase-onlyspatial light modulator (SLM), which is designed to shift the phase ofincident light by a programmable amount at each pixel in atwo-dimensional array. SLMs typically are designed to provide a range of2π radians of phase shift. Because a phase shift of 2π is equivalent toa zero phase shift, the helical profile, which covers an arbitrarilylarge range, can be mapped onto the device's dynamic range with themodulo operator: φ({right arrow over (ρ)})mod 2π. Light operated on byan SLM picks up the phase factor, exp(iφ({right arrow over (ρ)})) thatdistinguishes the helical beam in Equation (2) from a conventional beam.

The phase pattern that implements this mode conversion is an example ofa phase-only hologram. Whereas an SLM allows for dynamicallyreconfigured holograms, some data communications applications also cantake advantage of various optical elements such as microfabricateddiffractive optical elements (DOEs) with fixed phase transferproperties.

The helical phase function, represented in Equation (1), creates ahelical beam coaxial with the incident conventional beam. This modeconversion may not occur with perfect efficiency. The result maytherefore include an undiffracted portion of the original non-helicalbeam. To avoid this result, it may be desirable to deflect thediffracted helical beam. This can be accomplished by adding a phasefunction encoding a deflection by a wave vector {right arrow over (k)},φk({right arrow over (ρ)})={right arrow over (k)}·{right arrow over(ρ)},  (5)to the phase function encoding the mode conversion. The result is adeflected helical beam, with the undiffracted portion propagating in theundeflected direction.

FIG. 1 is a plot showing intensity profiles for superpositions ofhelical modes created from a conventional flattop beam with acomputer-designed phase-only DOE. The bold curve is computed for asuperposition of eight helical modes with topological charges l=11, 21,31, 41, 51, 61, 71, and 81. The thin curve is for a superposition withthe components at l=21 and 71 excluded. Rescaling the azimuthal averagesby the radial coordinate, r, makes clear that the superposed modes haveequal power.

Superpositions of helical modes are created generally as follows. In ageneral superposition,

$\begin{matrix}{{E\left( \overset{\rightarrow}{\rho} \right)} = {\sum\limits_{l = {- \infty}}^{\infty}{\alpha_{l}{\upsilon\left( \overset{\rightarrow}{\rho} \right)}{\exp\left( {{\mathbb{i}}\left\lbrack {{l\theta} + {{\overset{\rightarrow}{k}}_{l} \cdot \overset{\rightarrow}{\rho}} + \phi_{l}} \right\rbrack} \right)}}}} & (6)\end{matrix}$

created from a collimated beam with amplitude cross-section υ({rightarrow over (ρ)}). Even though the individual modes differ from the inputbeam by a pure phase factor, the sum also features amplitudemodulations. These amplitude modulations can be minimized, but might notbe altogether eliminated, by appropriately selecting the relativephases, φ_(l). Iterative and direct search algorithms are also availablefor computing phase-only holograms that can maximize diffraction intosuch superposed modes.

The data plotted with a bold curve in FIG. 1 were computed for asuperposition of eight modes ranging from l=11 to 81, created from asingle flat-top beam of light with a phase-only hologram. This plotshows the beam's intensity averaged over angles, scaled by thecircumference. Removing two modes from the superposition results in aclearly measurable change in the intensities associated with thosemodes, and a far less substantial change in other neighboring modes'intensities.

Using these methods, a single conventional laser beam or other lightsource can be transformed into a superposition of helical modes, eachtraveling in an independently specified direction. Possible exampleconfigurations include multiple modes propagating in the same direction,or beams with the same topological charge traveling in differentdirections.

A helical mode's topology endows it with an important property for datacommunications. Because all angles are present along the beam's axis,all phases are present. Typically, the resulting destructiveinterference causes the beam to be dark along its axis, regardless ofthe amplitude profile υ({right arrow over (ρ)}). The beam's intensity isredistributed into a ring of light of radius R_(l). The radius of thedark core increases with the beam's topological charge l. In the specialcase that the amplitude profile is that of a Laguerre-Gaussian eigenmodeof the Helmholtz equation, R_(l) is proportional to √{square root over(l)}. This is a conventional concept in the art (see, for example, M. J.Padgett and L. Allen. “The Poynting vector in Laguerre-Gaussian modes.”Optics Communications 121, 36-40 (1995)). More generally, for Gaussianbeams, flat-top beams, and other common profiles, it is conventionalthat R_(l) is proportional to l, (see, for example, J. E. Curtis and D.G. Grier. “Structure of optical vortices.” Physical Review Letters 90,133901 (2003)).

A photodetector 30 whose active area has dimensions substantiallysmaller than R_(l) for a given value of l will register no light whendirectly illuminated by a helical beam. After operation by the detectinghologram it is then a conventional beam and the beam would now activatethe photodetector. FIG. 2( a) is a representation showing how a helicalbeam 40 with topological charge l is converted to a conventionalnon-helical beam 50 by a DOE 60 encoding a topological charge of −l. Theresulting l=0 mode can be focused onto a photodetector 100 and measured.FIG. 2(b) shows how, if the DOE 60 does not exactly cancel the inputbeam's helicity, the resulting beam still has a dark focus and will notbe detected by the photodetector 100.

Recalling that diffractive optical elements are capable of changing abeam's topological charge suggests the method for specifically detectinglight in a particular topological mode depicted in FIGS. 2( a) and (b).The beam of light 40 is operated on by the diffractive optical element60 encoding a helical mode with topological charge −l. Any component ofthe beam 40 carrying topological charge l is thereby converted to anon-helical beam. After operation by the detecting hologram it is then aconventional beam 50 and the beam 50 can be focused to a bright spot.Other modes with l′≠l will be transformed to helical anodes withtopological charge l′−l ≠0 and will remain dark on axis. Distinguishingdifferent modes can be facilitated by focusing the DOE-transformed beamonto an aperture 110 that will block stray light from undesired modes,thereby improving the detector's selectivity.

Detecting helical modes does not suffer from limited diffractionefficiency to the same extent that creating them does. In particular, ifsome part of the selected helical mode is not operated on by thedetecting DOE photodetector 100, then that part will not be detected.Other modes will not be spuriously detected, however, so that faithfulmode detection can proceed with an imperfect form of the DOEphotodetector 100.

The same selectivity is obtained if the detection DOE 60 also deflectsthe beam of light 40. In this case, the detector 100 is centered on thedeflected beam's wave vector {right arrow over (k)}_(l) rather than theoriginal beam's optical axis. The detector's DOE can select and deflectdifferent modes into different directions, each of which can beoutfitted with a photodetector form of the detector 100. This permitsparallel detection of data encoded in superpositions of helical beams.For example, the eight modes projected in FIG. 1 can each be read outseparately by such a spatially resolved parallel topological detector.In practice, each of the superposed modes is deflected into all of thepossible output directions. Only the selected mode for a particulardirection focuses on the associated detector, however.

The simplest form of topological data communication is to modulate thetopological charge of a beam of light with a time-varying helicaldiffractive optical element and reading out the result with detectors100 such as those described in the previous section. Data can be encodedin the time-dependent sequence of topological charges in the beam, withthe simplest modulation involving switching between a state with l=0 andanother with l≠0. A more sophisticated approach encodes data in asequence of several values of l, each of which can be read out with aseparate topological charge detector. In a still more sophisticatedapproach, data can be encoded in multiple simultaneous topologicalchannels 200 using a superposition of helical states such as that inFIG. 1.

The detector 100 used to read out the topological charge also may betime-dependent, opening up the ability to hop among topological datachannels 200. This may be useful in applications akin to frequencyhopping in secure radio communications.

Beams of light that already carry data through other channels, such asamplitude modulation, wavelength modulation or phase modulation, alsocan be transformed into helical beams and superposed with other helicalbeams. Each data stream then is capable of traveling through aparticular topological channel in parallel with others.

In one implementation, a plurality of information carrying beams allilluminate an appropriately designed diffractive optical element, eachat a particular angle. The diffractive optical element deflects all ofthe beams into one or more selected directions, endowing each beam witha specific topological charge. The result is one or more beams carryinga superposition of different helical modes, each carrying informationencoded in other characteristics of the beam. This type of beam isreferred to as a topologically multiplexed beam.

The multiplexed beam can be demultiplexed with a similar DOE thatdissects the superposed beam into the individual constituents, one perthe topological channel 200. These reconstituted beams can be furtheranalyzed with other techniques. The simplest implementation of this ideawould use two copies of the same DOE, one to multiplex the beams, andanother turned backward to demultiplex it.

The system and method of the present invention can be incorporated intoa number of different applications. For example, a beam that alreadycarries multiple data channels can be taken to undergo wavelengthdivision multiplexing, where multiple wavelengths of light can be passedover a single fiber, to impress upon it a helical phase profile, therebymaking the beam amenable to topological multiplexing. Such a systemwould allow for a significantly increased number of topologicalchannels, resulting in a multiplication of the bandwidth of a particularcommunication channel 200.

Additionally, the present invention could also be used to create anencryption system. This encryption system may further be high high-speedand/or an all-optical encryption system. Furthermore, the superpositionof topological states itself can be used to convey information. Onecould also therefore encode information in the time-dependentsuperposition of topological modes, in addition to any other informationcarried within the input beams themselves. This can be used, forexample, to maintain an encoded checksum for the data carried on themultiple data channels to authenticate the sender of information. Thisprocess can constitute an additional, potentially secure, data channelin its own right. The present invention may provide for securityadvantages and advances in secure communication which deter or preventintrusion, eavesdropping, or unauthorized access, reception or decodingof transmitted information. The present invention may be used at leastin part for quantum communications, quantum cryptography, encoding ofclassical or quantum information, and in conjunction with varioustransmission media including free space communications.

In other embodiments of the invention various higher-order Gaussianbeams can be used as well as Laguerre-Gaussian (LG) modes, higher ordermodes, and/or orbital angular momentum.

In yet another embodiment the present invention may also employ variousoptical elements which include but are not limited to diffractiveoptical elements (DOEs) and which may further include microfabricateddiffractive DOEs with fixed phase transfer properties.

Further embodiments may include multiple transmitters and/or detectors,adaptive optics for such purposes as correction of degradation intransmission medium (e.g. fiber, air, etc) and may adjust for angularmisalignment or lateral misalignment (e.g. of transmitter and/orreceiver or detector).

While several embodiments have been shown and described herein, itshould be understood that changes and modifications can be made to theinvention without departing from the invention in its broader aspects.Various features of the invention are defined in the following claims:

1. A method of creating a topologically multiplexed light beam for usein optical data communications, comprising the steps of: providing atleast one information-carrying light beam having a phase, each of thelight beams illuminating a first optical element; using the firstoptical element to deflect the at least one information-carrying lightbeam into at least one selected direction; and providing the at leastone information-carrying light beam with a plurality of specifictopological charges imposed on the phase of the light beam, resulting inthe at least one multiplexed resultant light beam carrying asuperposition of different helical modes suitable for use in opticaldata communications via different topological channels.
 2. The method ofclaim 1 where the first optical element is a diffractive opticalelement.
 3. The method of claim 1 where illuminating the first opticalelement is done at a designated angle.
 4. The method of claim 1 whereindeflection of the information-carrying light beam comprises adding aphase function φk({right arrow over (ρ)})={right arrow over (k)}·{rightarrow over (ρ)}.
 5. The method of claim 1 further comprising the step ofusing a second optical element to dissect the at least one resultantbeam into a plurality of constituent beams.
 6. The method of claim 5wherein the first and second optical elements comprise at least twooptical elements, with the second optical element being orientedbackwards relative the first optical element on an optical axis.
 7. Themethod of claim 1 further including the step of processing at least oneof the information-carrying beam and the resultant light beam by atleast one of wavelength modulation, amplitude modulation, phasemodulation, and time pulse modulation.
 8. The method of claim 1 furtherincluding the step of generating a plurality of data channels from theresultant light beam.
 9. A method of providing topological datacommunication, comprising the steps of: providing a beam of light havinga phase and the beam of light for carrying information; imposing aplurality of topological charges on the phase of the beam of light;modulating the plurality of topological charges of the phase of the beamof light with an optical element to provide a multiplexed resultant databeam; and reading out the multiplexed resultant beam using a detector toprovide information for data communication.
 10. The method of claim 9where the optical element operates as at least one of a time-varyinghelical diffractive optical element (DOE) and a DOE with a fixed phasetransfer.
 11. The method of claim 9 wherein the optical elementintroduces a superposition of the plurality of topological charges, andwherein data is encoded in the sequence of topological charges, creatinga plurality of topological data channels.
 12. The method of claim 11where the sequence of topological charges is time-dependent.
 13. Themethod of claim 12 wherein the time-dependent sequence of topologicalcharges modulates between at least a first state and a second state. 14.The method of claim 11 further comprising the step of moving among theplurality of topological data channels using the time dependentdetector.
 15. The method of claim 9 further including the step selectedfrom the group consisting of at least one of Processing at the beam oflight, processing the data beam, performing a wavelength modulation,performing an amplitude modulation, performing a phase modulation andperforming a time pulse modulation.
 16. The method of claim 9 whereindata from the data beam is encoded in multiple simultaneous topologicalchannels using a superposition of helical states.
 17. The method ofclaim 9 wherein the detector operates in at least one of a timedependent manner and in a manner to detect an individual topologicalchannel of a plurality of topological channels disposed in parallel. 18.The method of claim 9 wherein the detector comprises a diffractiveoptical element.
 19. The method of claim 9 wherein the detectorcomprises a spatially resolved parallel topological detector.
 20. Themethod of claim 9 further including the step of processing at least oneof the information-carrying beam and the resultant light beam by atleast one of wavelength modulation, amplitude modulation, phasemodulation, and time pulse modulation.
 21. The method of claim 9 furtherincluding the step of generating a plurality of data channels from theresultant light beam.
 22. A method for transforming a beam of light intoa superposition of helical modes of light for use in optical datacommunications, comprising the steps of: providing a conventional beamof light having a phase; introducing a plurality of defects into thephase of the conventional beam of light, the defects creating amultiplexed helical beam of light coaxial with the conventional beam oflight, the conventional beam of light including an undiffracted portion;and deflecting the multiplexed helical beam of light away from theundiffracted portion of the conventional beam of light, thereby enablinguse of the multiplexed deflected helical beams for the optical datacommunications.
 23. The method of claim 22 wherein the conventional beamof light is transformed into a helical beam of light by passing theconventional beam of light through a transparent material with a helicalsurface relief.
 24. The method of claim 22 wherein the helical beam oflight is created by using a phase-only spatial light modulator to shiftthe phase of incident light by a designated amount at each pixel in atwo-dimensional array.
 25. The method of claim 24 wherein the helicalbeam of light is deflected by adding a phase function encoding adeflection by a wave vector to the phase shift imparted by the spatiallight modulator.
 26. The method of claim 22 further including the stepof processing at least one of the helical beam of light and theresultant light beam by at least one of wavelength modulation, amplitudemodulation, phase modulation, and time pulse modulation.
 27. The methodof claim 22 further including the step of generating a plurality of datachannels from the resultant light beam.
 28. A system for creating atopologically multiplexed light beam for use in optical datacommunications, comprising, a first optical element for acting on astarting light beam having a phase, the first optical elementconstructed to provide a selected plurality of topological charges tocreate an output light beam of at least one multiplexed resultant lightbeam carrying a superposition of different helical modes on themultiplexed resultant light beam; and a detector for sensing the outputlight beam, thereby enabling use of the multiplexed light beam foroptical data communications.
 29. The system as defined in claim 28further including a second optical element for operating on the outputlight beam to selectively deflect the output light beam.
 30. The systemas defined in claim 29 wherein the second optical element comprises atleast one of the first optical element and a focusing lens.
 31. Thesystem as defined in claim 28 wherein the detector comprises a spatiallysensitive sensor component for detecting the output light beam.
 32. Thesystem as defined in claim 31 wherein the spatially sensitive detectoris selected from the group consisting of a spatially resolved paralleltopological detector and a plurality of detectors.
 33. The system asdefined in claim 28 wherein the first optical element comprises adiffractive optical element (DOE) programmable by a computer.
 34. Thesystem as defined in claim 28 wherein the first optical element iscoupled to a computer which can dynamically program the first opticalelement to establish a changed form of the first optical element toproduce a different form of the topologically multiplexed light beam.35. The system as defined in claim 28 wherein the beam of lightcomprises at least one of wavelength multiplexed light, amplitudemodulated light, phase modulated light and time pulsed light formodulation by the optical element.
 36. The system as defined in claim 28wherein the output light beam includes a plurality of data channels. 37.A method for transforming a beam of light into a superposition ofhelical modes of light for use in optical data communications,comprising the steps of: providing a conventional beam of light having aphase; using a diffractive optical element to introduce a plurality ofdefects onto the phase of the conventional beam of light, the defectscreating a multiplexed helical beam of light coaxial with theconventional beam of light, the conventional beam of light including anundiffracted portion; and deflecting the multiplexed helical beam oflight away from the undiffracted portion of the conventional beam oflight, thereby enabling use of the deflected multiplexed helical beamsfor the optical data communications.
 38. The method of claim 37 whereinthe conventional beam of light is transformed into a helical beam oflight by passing the conventional beam of light through a transparentmaterial with a helical surface relief.
 39. The method of claim 37wherein the helical beam of light is created by using the diffractiveoptical element comprising a phase-only spatial light modulator to shiftthe phase of incident light by a designated amount at each pixel in atwo-dimensional array.
 40. The method of claim 39 wherein the helicalbeam of light is deflected by adding a phase function encoding adeflection by a wave vector to the phase shift imparted by the spatiallight modulator.
 41. The method of claim 37 further including the stepof processing at least one of the helical beam of light and theresultant light beam by using the diffractive optical element with atleast one of wavelength modulation, amplitude modulation, phasemodulation, and time pulse modulation.
 42. The method of claim 37further including the step of generating a plurality of data channelsfrom the resultant light beam.